It using Baker valve-gear might help narrow it down a bit.
This variant of Walschaert’s was used very widely in the USA but rarely if ever in the UK, where anyway most 4-4-0 locomotives had inside valve gear (typically Stephenson’s or Joy).
The 4-4-0 wheel arrangement was very common in 19C US practice but most of these engines too, seemed to have inside Stephenson’s Link Motion.
LBSC successfully used Baker Gear on one or two of his designs, including “Tich”.